Problem: Right now you are to solve a very, very simple problem — to crack the safe. Four positive integers stand one by one on a circle protecting the safe. You know that to unlock this striking safe you have to make all four numbers equal to one. Operations are as follows: you may choose two adjacent numbers and increase both by one; you may choose two adjacent even numbers and divide both by two. Nothing else. Crack the safe!

Input

The single line of the input contains four space-separated integer positive numbers not greater than 109 each — four numbers on the circle in consecutive order.

Output

The output should contain "-1" (quotes for clarity) if the safe is secure, that is it's impossible to crack it. Otherwise, output should contain the sequence of operations (one operations per line) leading to unlocking the safe. You don't have to minimize the number of operations, but it should not exceed 1000. To make things clear, assume numbers stand on positions 1 through 4. Each operation is encoded by two symbols. If the following operation is dividing then first symbol is '/'; otherwise it's '+' (addition). The second symbol is the position of the first number in pair in consecutive order. (see samples for clarification).

If there are several solutions, output any of them.

Examples

Input

1 1 1 1


Output



Input

1 2 4 2


Output

/2
/3


Input

3 3 1 1


Output

+1
/1
/1


Input

2 1 2 4


Output

/3
/4

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.InputMismatchException;

/**
 * @author Egor Kulikov (egor@egork.net)
 *         Created on 14.03.2010
 */
public class TaskC implements Runnable {
	private InputReader in;
	private PrintWriter out;

	public static void main(String[] args) {
//		new Thread(new Template()).start();
		new TaskC().run();
	}

	public TaskC() {
//		String id = getClass().getName().toLowerCase();
//		try {
//			System.setIn(new FileInputStream(id + ".in"));
//			System.setOut(new PrintStream(new FileOutputStream(id + ".out")));
//			System.setIn(new FileInputStream("input.txt"));
//			System.setOut(new PrintStream(new FileOutputStream("output.txt")));
//		} catch (FileNotFoundException e) {
//			throw new RuntimeException();
//		}
		in = new InputReader(System.in);
		out = new PrintWriter(System.out);
	}

	public void run() {
		int[] a = new int[6];
		for (int i = 0; i < 4; i++)
			a[i] = in.readInt();
		while (true) {
			int mx = a[0];
			for (int aa : a)
				mx = Math.max(aa, mx);
			if (mx == 1)
				break;
			int ind = -1;
			for (int i = 0; i < 4; i++) {
				if (a[i] % 2 == 0 && a[(i + 1) % 4] % 2 == 0) {
					ind = i;
					break;
				}
			}
			if (ind != -1) {
				half(a, ind);
				continue;
			}
			for (int i = 0; i < 4; i++) {
				if (a[i] % 2 == 1 && a[(i + 1) % 4] % 2 == 1 && (a[i] != 1 || a[(i + 1) % 4] != 1)) {
					ind = i;
					break;
				}
			}
			if (ind != -1) {
				plus(a, ind);
				continue;
			}
			for (int i = 0; i < 4; i++) {
				if (a[i] % 2 == 1 && a[i] != 1) {
					ind = i;
					break;
				}
			}
			if (ind != -1) {
				plus(a, ind);
				continue;
			}
			if (a[0] % 2 == 0 && a[2] % 2 == 0) {
				plus(a, 1);
				half(a, 0);
				continue;
			}
			if (a[1] % 2 == 0 && a[3] % 2 == 0) {
				plus(a, 2);
				half(a, 1);
				continue;
			}
			for (int i = 0; i < 4; i++) {
				if (a[i] != 1) {
					ind = i;
					break;
				}
			}
			if (a[ind] != 2) {
				plus(a, (ind + 1) % 4);
				half(a, ind);
				continue;
			}
			plus(a, ind);
			plus(a, (ind + 3) % 4);
			half(a, ind);
			half(a, (ind + 3) % 4);
		}
		out.close();
	}

	void plus(int[] a, int ind) {
		a[ind]++;
		a[(ind + 1) % 4]++;
		out.println("+" + (ind + 1));
	}

	void half(int[] a, int ind) {
		a[ind] /= 2;
		a[(ind + 1) % 4] /= 2;
		out.println("/" + (ind + 1));
	}

	private static class InputReader {
		private InputStream stream;
		private byte[] buf = new byte[1000];
		private int curChar, numChars;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		private int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int readInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public long readLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public String readString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuffer res = new StringBuffer();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private String readLine0() {
			StringBuffer buf = new StringBuffer();
			int c = read();
			while (c != '\n' && c != -1) {
				buf.appendCodePoint(c);
				c = read();
			}
			return buf.toString();
		}

		public String readLine() {
			String s = readLine0();
			while (s.trim().length() == 0)
				s = readLine0();
			return s;
		}

		public String readLine(boolean ignoreEmptyLines) {
			if (ignoreEmptyLines)
				return readLine();
			else
				return readLine0();
		}

		public BigInteger readBigInteger() {
			try {
				return new BigInteger(readString());
			} catch (NumberFormatException e) {
				throw new InputMismatchException();
			}
		}

		public char readCharacter() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			return (char) c;
		}

		public double readDouble() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') {
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) {
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}
	}
}